The TPC response calibration is performed with neutron and gamma sources and with gaseous \({^{83m}}\) Kr injected into the target volume [1]}. The S1 scintillation efficiency of nuclear recoils was measured with test beam experiments, namely SCENE [2]} and ARIS [3]}, and cross-calibrated with AmBe and AmC neutron sources
in DarkSide-50 [4]}.
The analysis uses both S1 and S2. S1 gives information on the nature of the event and
is the main energy variable. However, a combination of S1 and S2
gives an energy variable with better resolution and linearity, since
the deposited energy is shared between scintillation and ionization.
In addition, S2 determines the position and
rejects multiple scatter events.
Reference [5]} describes the procedure to calibrate the
nuclear-recoil energy scale from the scintillation
signal using the PE yield for nuclear recoils of known energy
measured in the SCENE experiment [2]}.
In summary, SCENE measures
the ratio between the PE yield from NR at 200 V/cm and that from \({^{83m}}\) Kr at
zero field. The DarkSide-50 zero-field PE yield for \({^{83m}}\) Kr
(8.0\(\pm \) 0.2 PE/keV [7]} measured at the peak energy of 41.5 keV) then gives the NR PE yield vs. S1. We assume constant NR PE yield above the highest
SCENE-measured energy, \(\sim 57.3\)  keV\(_{\mathrm {nr}}\) .
Monte Carlo simulations estimate that the
overall S1 light collection efficiency, averaged on the entire volume,
is about \(\sim \)  16%.
The analysis of the DarkSide-50 data is performed in blind mode as explained in Ref. [7]}.
The expected background events can be classified into three categories: surface events, neutrons (cosmogenic and radiogenic), and ERs. Surface events are mostly rejected with
fiducialization of the active volume, neutrons are efficiently suppressed with the LSV, and ERs are rejected with high efficiency using the \(f_{90}\)  parameter. The LSV, whose estimated efficiency is 0.9964\(\pm \) 0.0004, identified 4 neutron candidates. After the LSV cut, the dominant background comes from ERs (0.08\(\pm \) 0.04 surviving events). The \(f_{90}\)  acceptance requires a relatively large
nuclear-recoil threshold energy. The final acceptance is 60.9%, with a threshold energy \(\gtrsim \) 50 keV\(_{\mathrm {nr}}\)  (see Fig. 10 of Ref. [7]}) and the fiducial mass corresponds to 36.9\(\pm \) 0.6 kg.
The number of expected surviving background events for the entire statistics, which corresponds to (16660 \(\pm \)  270) kg d exposure, is \(0.09\pm 0.04\)  (for a detailed summary see Table V of Ref. [7]}).
After the data unblinding, no events were observed in the defined WIMP search region, as shown in Fig. 11 (right) of Ref. [7]}.
The lack of observed events is consistent with up to 2.3 WIMP-nucleon scatters expected at 90% C.L. and so can be used to draw 90% C.L. exclusion curves for the \(\sigma _i\)  cross sections in terms of the 12 realizations enumerated in Table REF , using a simple cut and counts statistical technique.
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